01 - Combine chicken, black beans, corn, red bell pepper, red onion, cheese, cilantro, cumin, chili powder, smoked paprika, salt, pepper, and lime juice in a large mixing bowl. Mix until evenly distributed throughout the mixture.
02 - Position an egg roll wrapper on a clean surface with one corner facing you in a diamond orientation. Place approximately 2 heaping tablespoons of filling on the lower third section of the wrapper.
03 - Fold the bottom corner over the filling, then fold both sides inward toward the center. Brush the remaining top corner with beaten egg and roll up tightly to create a secure seal. Repeat process for all remaining wrappers and filling.
04 - Pour vegetable oil to a depth of 2 inches in a deep skillet or fryer. Heat to 350°F, maintaining temperature throughout frying process.
05 - Cook egg rolls in small batches, allowing adequate space between pieces. Fry for 3 to 4 minutes, turning occasionally, until exterior reaches golden brown color and becomes crispy.
06 - Transfer cooked egg rolls to paper towel-lined surface to absorb excess oil. Allow to cool for several minutes before serving to prevent burns.
07 - Present with salsa, guacamole, or ranch dressing as desired accompaniments.